The relative biological effectiveness of low energy neutrons for the induction of various abnormalities in Tradescantia stamen hair mutation (Trad-SH) assay was studied using two clones (T-4430 and T-02), heterozygous for flower color. Dose response relationships for gene mutations induced in somatic cells of Trad-SH were investigated after irradiation with a mixed neutron beam of the Brookhaven Medical Research Reactor (BMRR), currently used in a clinical trial of boron neutron capture therapy (BNCT) for glioblastoma. To establish the RBE (relative biological effectiveness) of the BMRR beam in the induction of various biological end-points in Tradescantia, irradiation with various doses of g-rays was also performed. After irradiation all plants were cultivated several days at Brookhaven National Laboratory (BNL), the transported to Poland for screening the biological end-points. Due to the post-exposure treatment, all plants showed high levels of lethal events and alteration of the cell cycle. Plants of clone 4430 were more reactive to post-treatment conditions, resulting in decreased blooming efficiency that affected the statistics. Slope coefficients estimated from the dose response curves for gene mutation frequencies allowed the evaluation of ranges for the maximal RBE values of the applied beam vs. g-rays as 6.0 and 5.4 for the cells of T-02 and T-4430, respectively. Estimated fraction of doses from neutrons and corresponding biological effects for the clones T-02 and T-4430 allowed to evaluate the RBE values for neutrons part in the beam as 32.3 and 45.4, respectively.